TSTP Solution File: SET018-6 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET018-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 05:22:39 EDT 2022
% Result : Unsatisfiable 69.68s 69.97s
% Output : Refutation 71.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 26
% Syntax : Number of clauses : 141 ( 51 unt; 37 nHn; 141 RR)
% Number of literals : 257 ( 0 equ; 94 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(ordered_pair(y__dfg,z__dfg),ordered_pair(w__dfg,x__dfg)),
file('SET018-6.p',unknown),
[] ).
cnf(2,axiom,
member(x__dfg,universal_class),
file('SET018-6.p',unknown),
[] ).
cnf(3,axiom,
~ equal(z__dfg,x__dfg),
file('SET018-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET018-6.p',unknown),
[] ).
cnf(5,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET018-6.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET018-6.p',unknown),
[] ).
cnf(7,axiom,
subclass(u,universal_class),
file('SET018-6.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(u,v)
| subclass(v,u) ),
file('SET018-6.p',unknown),
[] ).
cnf(10,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET018-6.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET018-6.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(u,v)) ),
file('SET018-6.p',unknown),
[] ).
cnf(13,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(v,u)) ),
file('SET018-6.p',unknown),
[] ).
cnf(14,axiom,
member(unordered_pair(u,v),universal_class),
file('SET018-6.p',unknown),
[] ).
cnf(15,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET018-6.p',unknown),
[] ).
cnf(16,axiom,
equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v)),
file('SET018-6.p',unknown),
[] ).
cnf(18,axiom,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(v,x) ),
file('SET018-6.p',unknown),
[] ).
cnf(19,axiom,
( ~ member(u,v)
| ~ member(w,x)
| member(ordered_pair(w,u),cross_product(x,v)) ),
file('SET018-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET018-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET018-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET018-6.p',unknown),
[] ).
cnf(27,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET018-6.p',unknown),
[] ).
cnf(28,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET018-6.p',unknown),
[] ).
cnf(29,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('SET018-6.p',unknown),
[] ).
cnf(30,axiom,
equal(intersection(complement(intersection(u,v)),complement(intersection(complement(u),complement(v)))),symmetric_difference(u,v)),
file('SET018-6.p',unknown),
[] ).
cnf(69,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('SET018-6.p',unknown),
[] ).
cnf(70,axiom,
( equal(u,null_class)
| equal(intersection(u,regular(u)),null_class) ),
file('SET018-6.p',unknown),
[] ).
cnf(95,plain,
equal(intersection(complement(intersection(u,v)),union(u,v)),symmetric_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[29,30]),
[iquote('0:Rew:29.0,30.0')] ).
cnf(100,plain,
member(x__dfg,unordered_pair(x__dfg,u)),
inference(res,[status(thm),theory(equality)],[2,12]),
[iquote('0:Res:2.0,12.0')] ).
cnf(114,plain,
( ~ member(z__dfg,unordered_pair(u,x__dfg))
| equal(z__dfg,u) ),
inference(res,[status(thm),theory(equality)],[11,3]),
[iquote('0:Res:11.2,3.0')] ).
cnf(117,plain,
( ~ member(x__dfg,unordered_pair(u,z__dfg))
| equal(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[11,3]),
[iquote('0:Res:11.2,3.0')] ).
cnf(126,plain,
~ member(z__dfg,unordered_pair(x__dfg,x__dfg)),
inference(res,[status(thm),theory(equality)],[114,3]),
[iquote('0:Res:114.1,3.0')] ).
cnf(128,plain,
~ member(x__dfg,unordered_pair(z__dfg,z__dfg)),
inference(res,[status(thm),theory(equality)],[117,3]),
[iquote('0:Res:117.1,3.0')] ).
cnf(130,plain,
~ member(z__dfg,singleton(x__dfg)),
inference(rew,[status(thm),theory(equality)],[15,126]),
[iquote('0:Rew:15.0,126.0')] ).
cnf(132,plain,
~ member(x__dfg,singleton(z__dfg)),
inference(rew,[status(thm),theory(equality)],[15,128]),
[iquote('0:Rew:15.0,128.0')] ).
cnf(151,plain,
member(x__dfg,singleton(x__dfg)),
inference(spr,[status(thm),theory(equality)],[15,100]),
[iquote('0:SpR:15.0,100.0')] ).
cnf(153,plain,
member(singleton(u),universal_class),
inference(spr,[status(thm),theory(equality)],[15,14]),
[iquote('0:SpR:15.0,14.0')] ).
cnf(215,plain,
( ~ member(not_subclass_element(complement(u),v),u)
| subclass(complement(u),v) ),
inference(res,[status(thm),theory(equality)],[5,27]),
[iquote('0:Res:5.1,27.1')] ).
cnf(216,plain,
( subclass(u,u)
| subclass(u,u) ),
inference(res,[status(thm),theory(equality)],[5,6]),
[iquote('0:Res:5.1,6.0')] ).
cnf(217,plain,
subclass(u,u),
inference(obv,[status(thm),theory(equality)],[216]),
[iquote('0:Obv:216.0')] ).
cnf(240,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),v) ),
inference(res,[status(thm),theory(equality)],[5,25]),
[iquote('0:Res:5.1,25.0')] ).
cnf(255,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),u) ),
inference(res,[status(thm),theory(equality)],[5,24]),
[iquote('0:Res:5.1,24.0')] ).
cnf(355,plain,
( ~ member(unordered_pair(u,singleton(v)),universal_class)
| member(unordered_pair(u,singleton(v)),ordered_pair(u,v)) ),
inference(spr,[status(thm),theory(equality)],[16,13]),
[iquote('0:SpR:16.0,13.1')] ).
cnf(362,plain,
member(unordered_pair(u,singleton(v)),ordered_pair(u,v)),
inference(mrr,[status(thm)],[355,14]),
[iquote('0:MRR:355.0,14.0')] ).
cnf(365,plain,
member(unordered_pair(y__dfg,singleton(z__dfg)),ordered_pair(w__dfg,x__dfg)),
inference(spr,[status(thm),theory(equality)],[1,362]),
[iquote('0:SpR:1.0,362.0')] ).
cnf(373,plain,
( ~ member(not_subclass_element(u,complement(v)),universal_class)
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(res,[status(thm),theory(equality)],[28,6]),
[iquote('0:Res:28.2,6.0')] ).
cnf(406,plain,
( ~ subclass(universal_class,u)
| equal(universal_class,u) ),
inference(res,[status(thm),theory(equality)],[7,10]),
[iquote('0:Res:7.0,10.0')] ).
cnf(438,plain,
( ~ subclass(universal_class,u)
| member(unordered_pair(v,w),u) ),
inference(res,[status(thm),theory(equality)],[14,4]),
[iquote('0:Res:14.0,4.0')] ).
cnf(445,plain,
( ~ subclass(singleton(x__dfg),u)
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[151,4]),
[iquote('0:Res:151.0,4.0')] ).
cnf(460,plain,
( ~ subclass(u,v)
| subclass(u,w)
| member(not_subclass_element(u,w),v) ),
inference(res,[status(thm),theory(equality)],[5,4]),
[iquote('0:Res:5.1,4.0')] ).
cnf(485,plain,
( ~ member(ordered_pair(w__dfg,x__dfg),cross_product(u,v))
| member(z__dfg,v) ),
inference(spl,[status(thm),theory(equality)],[1,18]),
[iquote('0:SpL:1.0,18.0')] ).
cnf(504,plain,
( ~ equal(u,singleton(x__dfg))
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[9,445]),
[iquote('0:Res:9.1,445.0')] ).
cnf(507,plain,
~ equal(singleton(z__dfg),singleton(x__dfg)),
inference(res,[status(thm),theory(equality)],[504,132]),
[iquote('0:Res:504.1,132.0')] ).
cnf(583,plain,
( ~ member(u,symmetric_difference(v,w))
| member(u,complement(intersection(v,w))) ),
inference(spl,[status(thm),theory(equality)],[95,24]),
[iquote('0:SpL:95.0,24.0')] ).
cnf(603,plain,
( ~ member(u,singleton(v))
| equal(u,v)
| equal(u,v) ),
inference(spl,[status(thm),theory(equality)],[15,11]),
[iquote('0:SpL:15.0,11.0')] ).
cnf(604,plain,
( ~ member(u,ordered_pair(v,w))
| equal(u,unordered_pair(v,singleton(w)))
| equal(u,singleton(v)) ),
inference(spl,[status(thm),theory(equality)],[16,11]),
[iquote('0:SpL:16.0,11.0')] ).
cnf(619,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[603]),
[iquote('0:Obv:603.1')] ).
cnf(626,plain,
( subclass(singleton(u),v)
| equal(not_subclass_element(singleton(u),v),u) ),
inference(res,[status(thm),theory(equality)],[5,619]),
[iquote('0:Res:5.1,619.0')] ).
cnf(697,plain,
( ~ subclass(universal_class,complement(u))
| ~ member(unordered_pair(v,w),u) ),
inference(res,[status(thm),theory(equality)],[438,27]),
[iquote('0:Res:438.1,27.1')] ).
cnf(735,plain,
( ~ member(u,v)
| ~ member(u,w)
| ~ subclass(intersection(w,v),x)
| member(u,x) ),
inference(res,[status(thm),theory(equality)],[26,4]),
[iquote('0:Res:26.2,4.0')] ).
cnf(738,plain,
( ~ member(not_subclass_element(u,intersection(v,w)),w)
| ~ member(not_subclass_element(u,intersection(v,w)),v)
| subclass(u,intersection(v,w)) ),
inference(res,[status(thm),theory(equality)],[26,6]),
[iquote('0:Res:26.2,6.0')] ).
cnf(1330,plain,
( ~ member(x__dfg,u)
| ~ member(w__dfg,v)
| member(z__dfg,u) ),
inference(res,[status(thm),theory(equality)],[19,485]),
[iquote('0:Res:19.2,485.0')] ).
cnf(1621,plain,
( ~ member(not_subclass_element(complement(complement(u)),v),universal_class)
| member(not_subclass_element(complement(complement(u)),v),u)
| subclass(complement(complement(u)),v) ),
inference(res,[status(thm),theory(equality)],[28,215]),
[iquote('0:Res:28.2,215.0')] ).
cnf(3538,plain,
( ~ member(u,symmetric_difference(v,w))
| ~ member(u,intersection(v,w)) ),
inference(res,[status(thm),theory(equality)],[583,27]),
[iquote('0:Res:583.1,27.1')] ).
cnf(3569,plain,
( ~ member(not_subclass_element(intersection(u,complement(v)),w),v)
| subclass(intersection(u,complement(v)),w) ),
inference(res,[status(thm),theory(equality)],[240,27]),
[iquote('0:Res:240.1,27.1')] ).
cnf(3582,plain,
( subclass(intersection(u,v),v)
| subclass(intersection(u,v),v) ),
inference(res,[status(thm),theory(equality)],[240,6]),
[iquote('0:Res:240.1,6.0')] ).
cnf(3586,plain,
subclass(intersection(u,v),v),
inference(obv,[status(thm),theory(equality)],[3582]),
[iquote('0:Obv:3582.0')] ).
cnf(3669,plain,
( subclass(intersection(u,v),u)
| subclass(intersection(u,v),u) ),
inference(res,[status(thm),theory(equality)],[255,6]),
[iquote('0:Res:255.1,6.0')] ).
cnf(3673,plain,
subclass(intersection(u,v),u),
inference(obv,[status(thm),theory(equality)],[3669]),
[iquote('0:Obv:3669.0')] ).
cnf(3762,plain,
( ~ subclass(u,complement(v))
| ~ member(not_subclass_element(u,w),v)
| subclass(u,w) ),
inference(res,[status(thm),theory(equality)],[460,27]),
[iquote('0:Res:460.2,27.1')] ).
cnf(6203,plain,
( ~ subclass(u,universal_class)
| subclass(u,complement(v))
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(res,[status(thm),theory(equality)],[460,373]),
[iquote('0:Res:460.2,373.0')] ).
cnf(6207,plain,
( ~ subclass(u,universal_class)
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(obv,[status(thm),theory(equality)],[6203]),
[iquote('0:Obv:6203.1')] ).
cnf(6208,plain,
( member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(mrr,[status(thm)],[6207,7]),
[iquote('0:MRR:6207.0,7.0')] ).
cnf(8212,plain,
( ~ member(u,v)
| ~ member(u,w)
| member(u,universal_class) ),
inference(res,[status(thm),theory(equality)],[7,735]),
[iquote('0:Res:7.0,735.2')] ).
cnf(8222,plain,
( ~ member(u,v)
| member(u,universal_class) ),
inference(con,[status(thm)],[8212]),
[iquote('0:Con:8212.1')] ).
cnf(8299,plain,
( subclass(u,v)
| member(not_subclass_element(u,v),universal_class) ),
inference(res,[status(thm),theory(equality)],[5,8222]),
[iquote('0:Res:5.1,8222.0')] ).
cnf(8410,plain,
( member(not_subclass_element(complement(complement(u)),v),u)
| subclass(complement(complement(u)),v) ),
inference(mrr,[status(thm)],[1621,8299]),
[iquote('0:MRR:1621.0,8299.1')] ).
cnf(8973,plain,
( subclass(singleton(u),v)
| subclass(singleton(u),v)
| member(u,universal_class) ),
inference(spr,[status(thm),theory(equality)],[626,8299]),
[iquote('0:SpR:626.1,8299.1')] ).
cnf(8974,plain,
( subclass(complement(universal_class),u)
| subclass(complement(universal_class),u) ),
inference(res,[status(thm),theory(equality)],[8299,215]),
[iquote('0:Res:8299.1,215.0')] ).
cnf(8979,plain,
subclass(complement(universal_class),u),
inference(obv,[status(thm),theory(equality)],[8974]),
[iquote('0:Obv:8974.0')] ).
cnf(8981,plain,
( subclass(singleton(u),v)
| member(u,universal_class) ),
inference(obv,[status(thm),theory(equality)],[8973]),
[iquote('0:Obv:8973.0')] ).
cnf(10218,plain,
( ~ member(not_subclass_element(u,intersection(v,u)),v)
| subclass(u,intersection(v,u))
| subclass(u,intersection(v,u)) ),
inference(res,[status(thm),theory(equality)],[5,738]),
[iquote('0:Res:5.1,738.0')] ).
cnf(10232,plain,
( ~ member(not_subclass_element(u,intersection(v,u)),v)
| subclass(u,intersection(v,u)) ),
inference(obv,[status(thm),theory(equality)],[10218]),
[iquote('0:Obv:10218.1')] ).
cnf(12282,plain,
( ~ member(w__dfg,u)
| member(z__dfg,singleton(x__dfg)) ),
inference(res,[status(thm),theory(equality)],[151,1330]),
[iquote('0:Res:151.0,1330.0')] ).
cnf(12318,plain,
~ member(w__dfg,u),
inference(mrr,[status(thm)],[12282,130]),
[iquote('0:MRR:12282.1,130.0')] ).
cnf(12881,plain,
( ~ member(unordered_pair(u,v),universal_class)
| ~ subclass(universal_class,complement(unordered_pair(w,unordered_pair(u,v)))) ),
inference(res,[status(thm),theory(equality)],[13,697]),
[iquote('0:Res:13.1,697.1')] ).
cnf(12901,plain,
~ subclass(universal_class,complement(unordered_pair(u,unordered_pair(v,w)))),
inference(mrr,[status(thm)],[12881,14]),
[iquote('0:MRR:12881.0,14.0')] ).
cnf(14772,plain,
~ subclass(universal_class,complement(unordered_pair(u,singleton(v)))),
inference(spl,[status(thm),theory(equality)],[15,12901]),
[iquote('0:SpL:15.0,12901.0')] ).
cnf(17801,plain,
( subclass(complement(complement(u)),u)
| subclass(complement(complement(u)),u) ),
inference(res,[status(thm),theory(equality)],[8410,6]),
[iquote('0:Res:8410.0,6.0')] ).
cnf(17805,plain,
subclass(complement(complement(u)),u),
inference(obv,[status(thm),theory(equality)],[17801]),
[iquote('0:Obv:17801.0')] ).
cnf(17847,plain,
subclass(complement(union(u,v)),intersection(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[29,17805]),
[iquote('0:SpR:29.0,17805.0')] ).
cnf(20875,plain,
( subclass(u,intersection(universal_class,u))
| subclass(u,intersection(universal_class,u)) ),
inference(res,[status(thm),theory(equality)],[8299,10232]),
[iquote('0:Res:8299.1,10232.0')] ).
cnf(20877,plain,
( subclass(complement(complement(u)),intersection(u,complement(complement(u))))
| subclass(complement(complement(u)),intersection(u,complement(complement(u)))) ),
inference(res,[status(thm),theory(equality)],[8410,10232]),
[iquote('0:Res:8410.0,10232.0')] ).
cnf(20899,plain,
subclass(u,intersection(universal_class,u)),
inference(obv,[status(thm),theory(equality)],[20875]),
[iquote('0:Obv:20875.0')] ).
cnf(20925,plain,
subclass(complement(complement(u)),intersection(u,complement(complement(u)))),
inference(obv,[status(thm),theory(equality)],[20877]),
[iquote('0:Obv:20877.0')] ).
cnf(20961,plain,
( ~ subclass(intersection(universal_class,u),u)
| equal(intersection(universal_class,u),u) ),
inference(res,[status(thm),theory(equality)],[20899,10]),
[iquote('0:Res:20899.0,10.0')] ).
cnf(21176,plain,
equal(intersection(universal_class,u),u),
inference(mrr,[status(thm)],[20961,3586]),
[iquote('0:MRR:20961.0,3586.0')] ).
cnf(30696,plain,
( ~ subclass(u,complement(universal_class))
| subclass(u,v)
| subclass(u,v) ),
inference(res,[status(thm),theory(equality)],[8299,3762]),
[iquote('0:Res:8299.1,3762.1')] ).
cnf(30718,plain,
( ~ subclass(u,complement(universal_class))
| subclass(u,v) ),
inference(obv,[status(thm),theory(equality)],[30696]),
[iquote('0:Obv:30696.1')] ).
cnf(39260,plain,
( subclass(intersection(u,complement(universal_class)),v)
| subclass(intersection(u,complement(universal_class)),v) ),
inference(res,[status(thm),theory(equality)],[8299,3569]),
[iquote('0:Res:8299.1,3569.0')] ).
cnf(39280,plain,
subclass(intersection(u,complement(universal_class)),v),
inference(obv,[status(thm),theory(equality)],[39260]),
[iquote('0:Obv:39260.0')] ).
cnf(50033,plain,
( equal(unordered_pair(y__dfg,singleton(z__dfg)),unordered_pair(w__dfg,singleton(x__dfg)))
| equal(unordered_pair(y__dfg,singleton(z__dfg)),singleton(w__dfg)) ),
inference(res,[status(thm),theory(equality)],[365,604]),
[iquote('0:Res:365.0,604.0')] ).
cnf(53096,plain,
( equal(intersection(u,v),null_class)
| member(regular(intersection(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[69,24]),
[iquote('0:Res:69.1,24.0')] ).
cnf(53337,plain,
( ~ member(u,complement(universal_class))
| ~ member(u,v)
| member(u,w) ),
inference(res,[status(thm),theory(equality)],[39280,735]),
[iquote('0:Res:39280.0,735.2')] ).
cnf(53338,plain,
( ~ member(u,complement(universal_class))
| member(u,v) ),
inference(con,[status(thm)],[53337]),
[iquote('0:Con:53337.1')] ).
cnf(53452,plain,
( equal(u,null_class)
| subclass(null_class,u) ),
inference(spr,[status(thm),theory(equality)],[70,3673]),
[iquote('0:SpR:70.1,3673.0')] ).
cnf(53484,plain,
( ~ member(u,symmetric_difference(v,regular(v)))
| ~ member(u,null_class)
| equal(v,null_class) ),
inference(spl,[status(thm),theory(equality)],[70,3538]),
[iquote('0:SpL:70.1,3538.1')] ).
cnf(53498,plain,
subclass(null_class,u),
inference(mrr,[status(thm)],[53452,9]),
[iquote('0:MRR:53452.0,9.0')] ).
cnf(53508,plain,
( ~ subclass(u,null_class)
| equal(u,null_class) ),
inference(res,[status(thm),theory(equality)],[53498,10]),
[iquote('0:Res:53498.0,10.0')] ).
cnf(54105,plain,
equal(complement(universal_class),null_class),
inference(res,[status(thm),theory(equality)],[8979,53508]),
[iquote('0:Res:8979.0,53508.0')] ).
cnf(54123,plain,
( ~ subclass(u,null_class)
| subclass(u,v) ),
inference(rew,[status(thm),theory(equality)],[54105,30718]),
[iquote('0:Rew:54105.0,30718.0')] ).
cnf(54129,plain,
( ~ member(u,null_class)
| member(u,v) ),
inference(rew,[status(thm),theory(equality)],[54105,53338]),
[iquote('0:Rew:54105.0,53338.0')] ).
cnf(54157,plain,
( ~ member(u,null_class)
| equal(v,null_class) ),
inference(mrr,[status(thm)],[53484,54129]),
[iquote('0:MRR:53484.0,54129.1')] ).
cnf(54158,plain,
~ member(u,null_class),
inference(aed,[status(thm),theory(equality)],[3,54157]),
[iquote('0:AED:3.0,54157.1')] ).
cnf(54289,plain,
subclass(u,complement(null_class)),
inference(res,[status(thm),theory(equality)],[6208,54158]),
[iquote('0:Res:6208.0,54158.0')] ).
cnf(54304,plain,
equal(complement(null_class),universal_class),
inference(res,[status(thm),theory(equality)],[54289,406]),
[iquote('0:Res:54289.0,406.0')] ).
cnf(54380,plain,
equal(complement(intersection(universal_class,complement(u))),union(null_class,u)),
inference(spr,[status(thm),theory(equality)],[54304,29]),
[iquote('0:SpR:54304.0,29.0')] ).
cnf(54430,plain,
equal(complement(complement(u)),union(null_class,u)),
inference(rew,[status(thm),theory(equality)],[21176,54380]),
[iquote('0:Rew:21176.0,54380.0')] ).
cnf(54527,plain,
subclass(union(null_class,u),intersection(u,union(null_class,u))),
inference(rew,[status(thm),theory(equality)],[54430,20925]),
[iquote('0:Rew:54430.0,20925.0')] ).
cnf(56756,plain,
( member(u,universal_class)
| equal(singleton(u),null_class) ),
inference(res,[status(thm),theory(equality)],[8981,53508]),
[iquote('0:Res:8981.0,53508.0')] ).
cnf(56789,plain,
equal(singleton(w__dfg),null_class),
inference(res,[status(thm),theory(equality)],[56756,12318]),
[iquote('0:Res:56756.0,12318.0')] ).
cnf(56803,plain,
( equal(unordered_pair(y__dfg,singleton(z__dfg)),unordered_pair(w__dfg,singleton(x__dfg)))
| equal(unordered_pair(y__dfg,singleton(z__dfg)),null_class) ),
inference(rew,[status(thm),theory(equality)],[56789,50033]),
[iquote('0:Rew:56789.0,50033.1')] ).
cnf(56960,plain,
( ~ subclass(u,v)
| equal(intersection(u,w),null_class)
| member(regular(intersection(u,w)),v) ),
inference(res,[status(thm),theory(equality)],[53096,4]),
[iquote('0:Res:53096.1,4.0')] ).
cnf(58436,plain,
( ~ equal(null_class,u)
| subclass(u,v) ),
inference(res,[status(thm),theory(equality)],[9,54123]),
[iquote('0:Res:9.1,54123.0')] ).
cnf(64828,plain,
( ~ subclass(intersection(u,union(null_class,u)),union(null_class,u))
| equal(intersection(u,union(null_class,u)),union(null_class,u)) ),
inference(res,[status(thm),theory(equality)],[54527,10]),
[iquote('0:Res:54527.0,10.0')] ).
cnf(64839,plain,
equal(intersection(u,union(null_class,u)),union(null_class,u)),
inference(mrr,[status(thm)],[64828,3586]),
[iquote('0:MRR:64828.0,3586.0')] ).
cnf(78992,plain,
( ~ subclass(u,null_class)
| equal(intersection(u,v),null_class) ),
inference(res,[status(thm),theory(equality)],[56960,54158]),
[iquote('0:Res:56960.2,54158.0')] ).
cnf(79130,plain,
( ~ subclass(u,null_class)
| equal(union(null_class,u),null_class) ),
inference(spr,[status(thm),theory(equality)],[78992,64839]),
[iquote('0:SpR:78992.1,64839.0')] ).
cnf(79261,plain,
( ~ subclass(u,null_class)
| subclass(complement(null_class),intersection(complement(null_class),complement(u))) ),
inference(spr,[status(thm),theory(equality)],[79130,17847]),
[iquote('0:SpR:79130.1,17847.0')] ).
cnf(79389,plain,
( ~ subclass(u,null_class)
| subclass(universal_class,complement(u)) ),
inference(rew,[status(thm),theory(equality)],[21176,79261,54304]),
[iquote('0:Rew:21176.0,79261.1,54304.0,79261.1')] ).
cnf(80342,plain,
~ subclass(unordered_pair(u,singleton(v)),null_class),
inference(res,[status(thm),theory(equality)],[79389,14772]),
[iquote('0:Res:79389.1,14772.0')] ).
cnf(80809,plain,
~ equal(unordered_pair(u,singleton(v)),null_class),
inference(res,[status(thm),theory(equality)],[58436,80342]),
[iquote('0:Res:58436.1,80342.0')] ).
cnf(81688,plain,
equal(unordered_pair(y__dfg,singleton(z__dfg)),unordered_pair(w__dfg,singleton(x__dfg))),
inference(mrr,[status(thm)],[56803,80809]),
[iquote('0:MRR:56803.1,80809.0')] ).
cnf(86840,plain,
( ~ member(singleton(z__dfg),universal_class)
| member(singleton(z__dfg),unordered_pair(w__dfg,singleton(x__dfg))) ),
inference(spr,[status(thm),theory(equality)],[81688,13]),
[iquote('0:SpR:81688.0,13.1')] ).
cnf(86877,plain,
member(singleton(z__dfg),unordered_pair(w__dfg,singleton(x__dfg))),
inference(mrr,[status(thm)],[86840,153]),
[iquote('0:MRR:86840.0,153.0')] ).
cnf(86887,plain,
( equal(singleton(z__dfg),singleton(x__dfg))
| equal(singleton(z__dfg),w__dfg) ),
inference(res,[status(thm),theory(equality)],[86877,11]),
[iquote('0:Res:86877.0,11.0')] ).
cnf(86890,plain,
( ~ subclass(unordered_pair(w__dfg,singleton(x__dfg)),u)
| member(singleton(z__dfg),u) ),
inference(res,[status(thm),theory(equality)],[86877,4]),
[iquote('0:Res:86877.0,4.0')] ).
cnf(86892,plain,
equal(singleton(z__dfg),w__dfg),
inference(mrr,[status(thm)],[86887,507]),
[iquote('0:MRR:86887.0,507.0')] ).
cnf(86899,plain,
equal(unordered_pair(w__dfg,singleton(x__dfg)),unordered_pair(y__dfg,w__dfg)),
inference(rew,[status(thm),theory(equality)],[86892,81688]),
[iquote('0:Rew:86892.0,81688.0')] ).
cnf(86914,plain,
( ~ subclass(unordered_pair(y__dfg,w__dfg),u)
| member(w__dfg,u) ),
inference(rew,[status(thm),theory(equality)],[86892,86890,86899]),
[iquote('0:Rew:86892.0,86890.1,86899.0,86890.0')] ).
cnf(86915,plain,
~ subclass(unordered_pair(y__dfg,w__dfg),u),
inference(mrr,[status(thm)],[86914,12318]),
[iquote('0:MRR:86914.1,12318.0')] ).
cnf(86916,plain,
$false,
inference(unc,[status(thm)],[86915,217]),
[iquote('0:UnC:86915.0,217.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SET018-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.00/0.07 % Command : run_spass %d %s
% 0.07/0.25 % Computer : n028.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 600
% 0.07/0.25 % DateTime : Mon Jul 11 00:01:13 EDT 2022
% 0.07/0.25 % CPUTime :
% 69.68/69.97
% 69.68/69.97 SPASS V 3.9
% 69.68/69.97 SPASS beiseite: Proof found.
% 69.68/69.97 % SZS status Theorem
% 69.68/69.97 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 69.68/69.97 SPASS derived 64374 clauses, backtracked 4556 clauses, performed 33 splits and kept 26390 clauses.
% 69.68/69.97 SPASS allocated 138882 KBytes.
% 69.68/69.97 SPASS spent 0:01:09.56 on the problem.
% 69.68/69.97 0:00:00.02 for the input.
% 69.68/69.97 0:00:00.00 for the FLOTTER CNF translation.
% 69.68/69.97 0:00:00.78 for inferences.
% 69.68/69.97 0:00:05.64 for the backtracking.
% 69.68/69.97 0:01:02.24 for the reduction.
% 69.68/69.97
% 69.68/69.97
% 69.68/69.97 Here is a proof with depth 8, length 141 :
% 69.68/69.97 % SZS output start Refutation
% See solution above
% 71.15/71.41 Formulae used in the proof : prove_ordered_pair_determines_components2_1 prove_ordered_pair_determines_components2_2 prove_ordered_pair_determines_components2_3 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets equal_implies_subclass2 subclass_implies_equal unordered_pair_member unordered_pair2 unordered_pair3 unordered_pairs_in_universal singleton_set ordered_pair cartesian_product2 cartesian_product3 intersection1 intersection2 intersection3 complement1 complement2 union symmetric_difference regularity1 regularity2
% 71.15/71.41
%------------------------------------------------------------------------------